Preface....................................................................................................................xvii
Acknowledgments ...................................................................................................xix
Introduction .............................................................................................................xxi
PART I Introduction to Digital Signal and Image
Processing
Chapter 1 Signals and Biomedical Signal Processing .......................................... 3
1.1 Introduction and Overview........................................................3
1.2
What Is a “Signal”? ................................................................... 3
1.3 Analog, Discrete, and Digital Signals ....................................... 4
1.3.1 Analog Signals ............................................................. 4
1.3.2 Discrete Signals ............................................................ 4
1.3.3 Digital Signals ..............................................................6
1.4 Processing and Transformation of Signals ................................ 7
1.5 Signal Processing for Feature Extraction .................................. 8
1.6
Some Characteristics of Digital Images .................................... 9
1.6.1 Image Capturing ........................................................... 9
1.6.2 Image Representation ................................................... 9
1.6.3 Image Histogram ........................................................ 11
1.7 Summary ................................................................................. 13
Problems ............................................................................................. 13
Chapter 2 Fourier Transform .............................................................................. 15
2.1 Introduction and Overview...................................................... 15
2.2 One-Dimensional Continuous Fourier Transform................... 15
2.2.1 Properties of One-Dimensional Fourier Transform ....22
2.2.1.1 Signal Shift ................................................. 23
2.2.1.2 Convolution ................................................. 23
2.2.1.3 Linear Systems Analysis ............................24
2.2.1.4 Differentiation.............................................26
2.2.1.5 Scaling Property .........................................26
2.3 Sampling and Nyquist Rate .....................................................26
2.4 One-Dimensional Discrete Fourier Transform ....................... 27
2.4.1 Properties of DFT.......................................................28
2.5 Two-Dimensional Discrete Fourier Transform ....................... 31
Contents
vii
Acknowledgments ...................................................................................................xix
Introduction .............................................................................................................xxi
PART I Introduction to Digital Signal and Image
Processing
Chapter 1 Signals and Biomedical Signal Processing .......................................... 3
1.1 Introduction and Overview........................................................3
1.2
What Is a “Signal”? ................................................................... 3
1.3 Analog, Discrete, and Digital Signals ....................................... 4
1.3.1 Analog Signals ............................................................. 4
1.3.2 Discrete Signals ............................................................ 4
1.3.3 Digital Signals ..............................................................6
1.4 Processing and Transformation of Signals ................................ 7
1.5 Signal Processing for Feature Extraction .................................. 8
1.6
Some Characteristics of Digital Images .................................... 9
1.6.1 Image Capturing ........................................................... 9
1.6.2 Image Representation ................................................... 9
1.6.3 Image Histogram ........................................................ 11
1.7 Summary ................................................................................. 13
Problems ............................................................................................. 13
Chapter 2 Fourier Transform .............................................................................. 15
2.1 Introduction and Overview...................................................... 15
2.2 One-Dimensional Continuous Fourier Transform................... 15
2.2.1 Properties of One-Dimensional Fourier Transform ....22
2.2.1.1 Signal Shift ................................................. 23
2.2.1.2 Convolution ................................................. 23
2.2.1.3 Linear Systems Analysis ............................24
2.2.1.4 Differentiation.............................................26
2.2.1.5 Scaling Property .........................................26
2.3 Sampling and Nyquist Rate .....................................................26
2.4 One-Dimensional Discrete Fourier Transform ....................... 27
2.4.1 Properties of DFT.......................................................28
2.5 Two-Dimensional Discrete Fourier Transform ....................... 31
Contents
vii